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4014 12
PM guideway I
90
36
9
16
PM guideway C
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33
10
16
PM guideway B
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2714 18
PM guideway A
Optimization of the Superconducting Linear
Magnetic Bearing of a Maglev Vehicle
Loïc Quéval
1
, Guilherme G. Sotelo
2
, Y. Kharmiz
1
, Daniel H.N. Dias
2
, Felipe Sass
2
,
Purpose
1 Lab for Electrical Machines, University of Applied Sciences, Düsseldorf, Germany.
2 Fluminense Federal University, Niterói (RJ), Brazil.
3 Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
Develop and validate a 3D FE model of a superconducting linear magnetic bearing.
Reduce the 3D model to a 2D model to decrease the computing time while keeping a good accuracy.
Use the 2D model to optimize the bearing cost considering a displacement sequence.
Modeling
PM guideway model
Conclusion
We developed a superconducting linear magnetic bearing 3D finite element model. It is
based on the H-formulation with a power law E-J relationship. The J
c
(B) dependence, the PM
guideway real geometry and the iron nonlinearity are included. The model is validated by
comparison with experimental data. For the optimization, the 3D model is reduced to a 2D
model by shortening artificially its length, instead of decreasing the critical current density.
Taking the SupraTrans prototype bearing as reference, the PM guideway optimization results
show that it is possible to greatly reduce the cost for the same performances on a given
displacement sequence; or to greatly improve the performances for the same cost.
Víctor M.R. Zermeno
3
, Raimund Gottkehaskamp
1
ID: 3A-LS-P-04.03
From 3D to 2D
It is common practice to calibrate the critical current density J
c0
of the bulk using the
maximum levitation force measured during the ZFC sequence.
Parametrization
We consider the bearing initially designed and optimized for the SupraTrans maglev vehicle
demonstrator.
HTS bulk model
SLMB model
(a) Zero field cooling
(b) Vertical displacement downward
(c) Vertical displacement upward.
(a) Field cooling
(b) Vertical displacement downward
(c) Lateral displacements.
Validation
What: Permanent magnets and iron pieces
arranged in flux concentrator.
How: 2D magnetostatic FEM
- iron nonlinear BH curve
- real geometry.
What: 3-seeded melt-textured YBCO block.
How: 2D or 3D H-formulation FEM
- power law E-J relationship
- isotropic Kim like model Jc(B)
- 3 independent domains.
How: Unidirectional coupling between HTS bulk
model and PM guideway model.
- only 1 static solution of the PM guideway model
- reduced LN
2
domain around HTS bulk.
Objective and constraints
Optimization
3D model 2D model
with reduced J
c0
with reduced d
Results
2D model
Dimensions of PM guideway : 4 parameters
Dimensions of HTS bulk : unchanged
Computing time < 1 min
We look for the PM guideways that minimize the cost of the guideway and maximize the
lateral force during LD sequence, with a constraint on the minimum levitation force,
Multi-objective Particule Swarm Optimization (PSO)
- 100 particules
- 25 generations
Total computing time ~40 h
Optimization algorithm
Fig. 1 - SLMB Geometry.
Fig. 2 - Magnetic flux density above the PM guideway
at z = 1, 5, 10, 20 mm.
Fig. 3 - Levitation force for ZFC sequence.
Fig. 4 - Lateral force for LD sequence.
Fig. 5 - Levitation force for LD sequence.
Note: The decrease of the levitation force during lateral displacements should be taken into
account during the optimization.
"Optimization on a displacement sequence"
5 mm
ZFC sequence
LD sequence
5 mm
25 mm 100 mm
10 mm
Fig. 8 - Initial and optimized PM guideways.
Dimensions in mm (on scale).
with
where , , .
cost [€/m]
F
y,max
[N]
PM guideway I
PM guideway A
PM guideway B
PM guideway C
1005
1012
1628
83
83
129
776
-23 %
99
+38 %
Fig. 7 - Bi-objective optimization results.
~
Fig. 6 - Parametrization of the PM guideway.
b
ac d
